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A payoff function for a player is a mapping from the cross-product of players' strategy spaces to that player's set of payoffs (normally the set of real numbers, where the number represents a cardinal or ordinal utility—often cardinal in the normal-form representation) of a player, i.e. the payoff function of a player takes as its input a ...
When academics talk about coordination failure, most cases are that subjects achieve risk dominance rather than payoff dominance. Even when payoffs are better when players coordinate on one equilibrium, many times people will choose the less risky option where they are guaranteed some payoff and end up at an equilibrium that has sub-optimal payoff.
The excess of for a coalition is the quantity (); that is, the gain that players in coalition can obtain if they withdraw from the grand coalition under payoff and instead take the payoff (). The nucleolus of v {\displaystyle v} is the imputation for which the vector of excesses of all coalitions (a vector in R 2 N {\displaystyle \mathbb {R ...
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Risk dominance and payoff dominance are two related refinements of the Nash equilibrium (NE) solution concept in game theory, defined by John Harsanyi and Reinhard Selten.A Nash equilibrium is considered payoff dominant if it is Pareto superior to all other Nash equilibria in the game. 1 When faced with a choice among equilibria, all players would agree on the payoff dominant equilibrium since ...
"A best response to a coplayer’s strategy is a strategy that yields the highest payoff against that particular strategy". [9] A matrix is used to present the payoff of both players in the game. For example, the best response of player one is the highest payoff for player one’s move, and vice versa.
Suppose a zero-sum game has a payoff matrix M where element M i,j is the payoff obtained when the minimizing player chooses pure strategy i and the maximizing player chooses pure strategy j (i.e. the player trying to minimize the payoff chooses the row and the player trying to maximize the payoff chooses the column).
Payoff functions, u: Assign a payoff to a player given their type and the action profile. A payoff function, u= (u 1 , . . . , u N ) denotes the utilities of player i Prior, p : A probability distribution over all possible type profiles, where p(t) = p(t 1 , . . . ,t N ) is the probability that Player 1 has type t 1 and Player N has type t N .